Mathematics
The sum of the numerator and the denominator of a fraction is equal to 7. Four times the numerator is 8 less than 5 times the denominator. Find the fraction.
Linear Equations
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Answer
Let numerator be x and denominator be y.
Given,
Sum of the numerator and the denominator of a fraction is equal to 7.
∴ x + y = 7
⇒ x = 7 - y ……….(1)
Given,
Four times the numerator is 8 less than 5 times the denominator.
⇒ 5y - 4x = 8 ………(2)
Substituting value of x from equation (1) in equation (2), we get :
⇒ 5y - 4(7 - y) = 8
⇒ 5y - 28 + 4y = 8
⇒ 9y = 8 + 28
⇒ 9y = 36
⇒ y = = 4
Substituting value of y in equation (1), we get :
⇒ x = 7 - 4 = 3.
Fraction = .
Hence, fraction = .
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